where \(Ê\text{sn}(u\vert m)\)  and \(\text{dn}(u \vert m)\)  are Jacobian elliptic functions and \(K\equiv K(m)\)  is the complete elliptic integral of first kind [1]}. Using the Fourier representation of elliptic fonctions [1]}, we find,
\(\sin (x) =2 \left\lbrace  \frac{2\pi }{K} \sum _{n=0}^{+\infty } \frac{q^{n+1/2}}{1-q^{2n+1}} \sin [(2n+1)\theta ] \right\rbrace  \times \left\lbrace \frac{\pi }{2K}+\frac{2\pi }{K} \sum _{n=1}^{+\infty } \frac{q^{n}}{1+q^{2n}} \cos [2n\theta ] \right\rbrace ,\) 
